Gas Laws and Atmospheric Variables Questions and Answers

Answer: A

The exponent \( R/c_p \) equals 287 divided by 1005, or about 0.286, and it follows directly from integrating the first law for an adiabatic process. It is sometimes written as kappa. The ratio of specific heats gamma equals 1.4 and is related but distinct, since \( R/c_p = (\gamma-1)/\gamma \). Confusing the two is a frequent source of error.

Answer: B

The value 1005 joules per kilogram per kelvin applies at constant pressure, while the constant volume value is 718, and the two differ by exactly the specific gas constant of 287. That relationship, \( c_p - c_v = R \), is a useful check on any set of remembered values. Liquid water has a far larger specific heat, which is why the oceans dominate the heat capacity of the climate system. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Answer: C

For an ideal gas \( c_p - c_v = R \), which follows from the definition of enthalpy and the equation of state. With 1005 and 718 for dry air the difference is 287, exactly the specific gas constant. This identity is worth carrying because it allows any one of the three constants to be recovered from the other two when memory fails.

Answer: D

The ratio \( \gamma = c_p/c_v \) equals 1005 divided by 718, or about 1.4, which is the value expected for a gas of diatomic molecules with five active degrees of freedom. The other values listed are kappa and epsilon, both of which appear frequently in the same formulae and are easily confused with gamma. Tracing each back to its definition prevents the confusion. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: A

The saturation vapour pressure over a plane water surface at 0 degrees Celsius is 6.11 hectopascals, which is also very nearly the triple point pressure of water. It roughly doubles for every 10 kelvin of warming, reaching about 23 hectopascals at 20 degrees and 42 at 30. Those few anchor values allow a rapid mental estimate of the moisture content of any air sample. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Answer: B

Clausius and Clapeyron derived the relation from the equality of the Gibbs functions of the two phases, giving a saturation vapour pressure that increases roughly exponentially with temperature. The rate is about 7 per cent per kelvin near terrestrial temperatures. It is the single most important relation in moist thermodynamics and underlies projections of increasing extreme rainfall in a warming climate. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: C

The saturation vapour pressure rises about 7 per cent for each kelvin near terrestrial temperatures, which corresponds to a doubling for roughly every 10 kelvin. That single number underlies the water vapour feedback, the intensification of extreme rainfall and the shape of the moist adiabat. It varies slowly with temperature but 7 per cent is a good working value across the relevant range. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: D

Below zero degrees the saturation vapour pressure over ice is lower than over supercooled water, with the difference reaching a maximum near minus 12 degrees. This is the basis of the Bergeron process, in which ice crystals grow at the expense of surrounding droplets. Without that difference, precipitation formation in mid-latitude clouds would be far less efficient. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: A

In a mixed phase cloud the air is supersaturated with respect to ice while being only just saturated with respect to water, so ice crystals grow rapidly while droplets evaporate. This is the dominant precipitation mechanism in mid-latitude clouds. Collision and coalescence dominates in warm tropical clouds containing no ice, so both mechanisms operate but in different environments. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: B

The two curves coincide at 0 degrees and converge again at very low temperatures, with the maximum difference near minus 12 degrees. That is why the Bergeron process operates most efficiently in that temperature range, and why the layer between about minus 10 and minus 20 degrees is so important for precipitation formation. At minus 40 all supercooled water has frozen and no mixed phase cloud remains. Most errors here come from carrying a result across from a neighbouring case where it does not hold.